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We investigate the twist-3 light-cone distribution amplitudes (LCDAs) of thescalar mesons $a_0$, $K^{\ast}_0$ and $f_0$ within the QCD sum rules. The QCDsum rules are improved by a consistent treatment of the sizable $s$-quark masseffects within the framework of the background field approach. Adopting thevalence quark component $(\bar{q}_1 q_2)$ as the dominant structure of thescalar mesons, our estimation for their masses are close to the measured$a_0(1450)$, $K^{\ast}_0(1430)$ and $f_0(1710)$. From the sum rules, we obtainthe first two non-zero moments of the twist-3 LCDAs $\phi^{s,\sigma}_{a_0}$:$\langle \xi_{s,a_0}^{2(4)} \rangle=0.369 \;(0.245)$ and $\langle\xi_{\sigma,a_0}^{2(4)} \rangle=0.203 \;(0.093)$; those of the twist-3 LCDAs$\phi_{K^*_0}^{s,\sigma}$: $\langle \xi_{s,K^{\ast}_0}^{1(2)} \rangle=0.004\;(0.355)$ and $\langle \xi_{\sigma,K^{\ast}_0}^{1(2)} \rangle=0.018\;(0.207)$; and those of the twist-3 LCDAs $\phi_{f_0}^{s,\sigma}$:$\langle \xi_{s,f_0}^{2(4)} \rangle=0.335 \;(0.212)$ and $\langle\xi_{\sigma,f_0}^{2(4)} \rangle=0.196 \; (0.088)$, respectively. As anapplication of those twist-3 LCDAs, we study the $B \to S$ transition formfactors by introducing proper chiral currents into the correlator, which isconstructed such that the twist-3 LCDAs give dominant contribution and thetwist-2 LCDAs make negligible contribution. Our results of the $B \to S$transition form factors at the large recoil region $q^2 \simeq 0$ areconsistent with those obtained in the literature, which inversely shows thepresent twist-3 LCDAs are acceptable.

european physical journal. a, hadrons and nuclei

Twist-3 light-cone distribution amplitudes of the scalar mesons within  the QCD sum rules and their application to the $B \to S$ transition form  factors